The aim of these exercises is to continue making sure you’re
comfortable with handling multivariate data. In this chapter’s, you’ll
focus on analyses based on dissimilarities/distances, including fitting
linear models to these kinds of response variables.
For each of the examples below, you should follow the sequence we’ve
used previously, as far as it’s sensible:
What is the biological question?
Is the predictor continuous or categorical?
Write out the linear model corresponding to this
question.
What distribution do you expect the response variable to
follow?
What are the assumptions behind the statistical model you’ll
fit?
- Are those assumptions satisfied?
Fit the model
How will you assess whether the model fits well?
Can you detect an effect of the predictors?
How do you measure the effect?
What do you conclude (including any cautions)
A
Dixon et al. (2018) focused on
assemblages of reptiles in forests and woodlands of southeastern
Australia, with a particular interest in relationships between these
assemblages and the fire history of the landscape. They identified 81
sites that varied in time since fire, from 6 months to >96 y. Rather
than a continuum, three categories of time since fire were used, 0.5-2y,
6-12y, and >96y. Sites were also classified according to habitat.
Reptile assemblages were sampled with a range of methods, including
visual surveys and camera traps, to give counts of 20 reptiles, whose
abundance ranged from 0-1 to 0-126, depending on species.
Data are available from dryad,
as Rep_abund.csv. You’ll want to focus on the columns with reptile
numbers, and the one with the fire history (tsf). For convenience, we’ve
extracted those data as dixonbiota.csv
Start by having a quick look at the data.
Rows: 79 Columns: 22── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): site, tsf
dbl (20): adup, aplat, amur, amac, aram, dcor, ecun, esax, eul, htal, ldel, lgui, lwhi, ppor, pent, pspe, ptex, rdie, tnig, vros
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
The file is pretty straightforward, with tsf being the fire category,
and columns 3-22 each representing one reptile taxon.
Outline how you’d assess whether the reptile assemblage (the
combination of species present and their abundances) is related to fire
history, using a dissimilarity-based approach.
You should think about how you’ll deal with the data:
Will you need a transformation, standardization, etc.?
What are the consequences of any decisions you make for the
interpretation of your analysis?
What measure(s) of dissimilarity are appropriate?
Run the analysis and provide your interpretation
MDS on reptile abundances
Start with dissimilarities
Students should have some discussion of raw vs transformed (e.g. 4th
root), standardization.
Fourth root is common. Using it downweights the influence of abundant
species, while raw allows those species to have a strong influence.
There are questions about which one of these reflects ecological
function better
Data are all abundances
Visualize results
Need to decide whether to use 2 or 3 dimensions
Run 0 stress 0.184364
Run 1 stress 0.1954244
Run 2 stress 0.1835248
... New best solution
... Procrustes: rmse 0.02400721 max resid 0.1627118
Run 3 stress 0.1875543
Run 4 stress 0.1873871
Run 5 stress 0.1835255
... Procrustes: rmse 0.0002431954 max resid 0.001211121
... Similar to previous best
Run 6 stress 0.1835255
... Procrustes: rmse 0.0004322375 max resid 0.002396493
... Similar to previous best
Run 7 stress 0.187394
Run 8 stress 0.1839905
... Procrustes: rmse 0.01513281 max resid 0.1010331
Run 9 stress 0.1835253
... Procrustes: rmse 0.0003986974 max resid 0.002827447
... Similar to previous best
Run 10 stress 0.1875557
Run 11 stress 0.1835394
... Procrustes: rmse 0.00239692 max resid 0.01890764
Run 12 stress 0.1875561
Run 13 stress 0.1962511
Run 14 stress 0.1845587
Run 15 stress 0.1835253
... Procrustes: rmse 0.0007731379 max resid 0.004859597
... Similar to previous best
Run 16 stress 0.1855483
Run 17 stress 0.1901239
Run 18 stress 0.1876739
Run 19 stress 0.1874628
Run 20 stress 0.1837457
... Procrustes: rmse 0.009486057 max resid 0.06288526
Run 21 stress 0.1835247
... New best solution
... Procrustes: rmse 0.000444541 max resid 0.003456569
... Similar to previous best
Run 22 stress 0.1835247
... Procrustes: rmse 0.000423645 max resid 0.0032015
... Similar to previous best
Run 23 stress 0.1893602
Run 24 stress 0.1873867
Run 25 stress 0.1853823
Run 26 stress 0.1923026
Run 27 stress 0.1839242
... Procrustes: rmse 0.01343186 max resid 0.08937936
Run 28 stress 0.1880216
Run 29 stress 0.1875504
Run 30 stress 0.1844798
Run 31 stress 0.1835267
... Procrustes: rmse 0.001099299 max resid 0.00825338
... Similar to previous best
Run 32 stress 0.1880227
Run 33 stress 0.1880842
Run 34 stress 0.1874227
Run 35 stress 0.1835265
... Procrustes: rmse 0.000828435 max resid 0.006610793
... Similar to previous best
Run 36 stress 0.1835258
... Procrustes: rmse 0.0009260963 max resid 0.007366734
... Similar to previous best
Run 37 stress 0.1875538
Run 38 stress 0.1880843
Run 39 stress 0.1844375
Run 40 stress 0.1835246
... New best solution
... Procrustes: rmse 5.771551e-05 max resid 0.0002761158
... Similar to previous best
*** Best solution repeated 1 times

Call:
metaMDS(comm = df1s.bc, k = 3, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1s.bc
Distance: bray
Dimensions: 3
Stress: 0.1835246
Stress type 1, weak ties
Best solution was repeated 1 time in 40 tries
The best solution was from try 40 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Run 0 stress 0.2620287
Run 1 stress 0.2657228
Run 2 stress 0.2613208
... New best solution
... Procrustes: rmse 0.03050854 max resid 0.1997569
Run 3 stress 0.2634799
Run 4 stress 0.255339
... New best solution
... Procrustes: rmse 0.08914296 max resid 0.2703881
Run 5 stress 0.2585276
Run 6 stress 0.2557278
... Procrustes: rmse 0.008721101 max resid 0.04949448
Run 7 stress 0.2557123
... Procrustes: rmse 0.007310089 max resid 0.03878651
Run 8 stress 0.2553666
... Procrustes: rmse 0.0102181 max resid 0.07939793
Run 9 stress 0.2700152
Run 10 stress 0.2644649
Run 11 stress 0.2626207
Run 12 stress 0.2629297
Run 13 stress 0.2650439
Run 14 stress 0.268519
Run 15 stress 0.2684536
Run 16 stress 0.2622278
Run 17 stress 0.2692256
Run 18 stress 0.268778
Run 19 stress 0.2643455
Run 20 stress 0.2607326
Run 21 stress 0.2685011
Run 22 stress 0.2637274
Run 23 stress 0.2652818
Run 24 stress 0.2717004
Run 25 stress 0.2597301
Run 26 stress 0.258373
Run 27 stress 0.2629686
Run 28 stress 0.2736616
Run 29 stress 0.2573166
Run 30 stress 0.3044425
Run 31 stress 0.2715289
Run 32 stress 0.2585135
Run 33 stress 0.2618396
Run 34 stress 0.2557593
... Procrustes: rmse 0.01141604 max resid 0.06725798
Run 35 stress 0.2567309
Run 36 stress 0.2621995
Run 37 stress 0.2556597
... Procrustes: rmse 0.007557198 max resid 0.03638444
Run 38 stress 0.2661423
Run 39 stress 0.2621501
Run 40 stress 0.2626279
Run 41 stress 0.2638528
Run 42 stress 0.2666209
Run 43 stress 0.2552761
... New best solution
... Procrustes: rmse 0.003378444 max resid 0.0214193
Run 44 stress 0.2643959
Run 45 stress 0.2559259
Run 46 stress 0.2702403
Run 47 stress 0.2743521
Run 48 stress 0.2639517
Run 49 stress 0.2674239
Run 50 stress 0.2660627
Run 51 stress 0.260206
Run 52 stress 0.259709
Run 53 stress 0.2695475
Run 54 stress 0.2652297
Run 55 stress 0.2669659
Run 56 stress 0.2695288
Run 57 stress 0.2585219
Run 58 stress 0.2553393
... Procrustes: rmse 0.003381346 max resid 0.02138202
Run 59 stress 0.2635542
Run 60 stress 0.2603403
Run 61 stress 0.2665924
Run 62 stress 0.2673204
Run 63 stress 0.2627007
Run 64 stress 0.2691563
Run 65 stress 0.2634604
Run 66 stress 0.2557524
... Procrustes: rmse 0.01015447 max resid 0.06110719
Run 67 stress 0.2587965
Run 68 stress 0.2600645
Run 69 stress 0.2673046
Run 70 stress 0.2636262
Run 71 stress 0.2629212
Run 72 stress 0.2569404
Run 73 stress 0.2587754
Run 74 stress 0.2628626
Run 75 stress 0.2662464
Run 76 stress 0.2693245
Run 77 stress 0.2701223
Run 78 stress 0.2646634
Run 79 stress 0.2667217
Run 80 stress 0.2666245
*** Best solution was not repeated -- monoMDS stopping criteria:
13: no. of iterations >= maxit
67: stress ratio > sratmax

Call:
metaMDS(comm = df1s.bc, k = 2, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1s.bc
Distance: bray
Dimensions: 2
Stress: 0.2552761
Stress type 1, weak ties
Best solution was not repeated after 80 tries
The best solution was from try 43 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Stress values suggest 3d plot is a more accurate representation
Need to plot dim 1 vs dim 2 and dim 1 vs dim 3 with tsf groups
identified by symbols
Generate graphs
This is a variant of code used in worked example for Ch 16. It does
use the graph settings defined in appearance.R, which is called
earlier.

How would you fit a linear model to assess fire effects?
Do permanova including tsf
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
adonis2(formula = df1s.bc ~ tsf, data = df, permutations = 999)
Df SumOfSqs R2 F Pr(>F)
tsf 2 2.6433 0.11039 4.7151 0.001 ***
Residual 76 21.3028 0.88961
Total 78 23.9460 1.00000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Permanova suggests strong signal from tsf
SIMPER analysis for tsf group differences
Contrast: long_short
average sd ratio ava avb cumsum p
lgui 0.13247 0.14056 0.94250 0.15918 0.26922 0.172 0.3247
eul 0.09332 0.12167 0.76700 0.02379 0.16793 0.293 0.0430 *
dcor 0.08201 0.11054 0.74190 0.06582 0.10672 0.399 0.1219
amac 0.06242 0.05874 1.06250 0.07712 0.07023 0.480 0.9760
tnig 0.05948 0.07551 0.78760 0.03804 0.07852 0.557 0.8492
ldel 0.05168 0.04157 1.24340 0.08687 0.00000 0.624 0.0010 ***
pent 0.05090 0.04718 1.07890 0.10975 0.03392 0.690 0.7133
htal 0.03859 0.05635 0.68490 0.04599 0.02950 0.740 0.4176
lwhi 0.03208 0.03938 0.81470 0.04549 0.01261 0.782 0.0160 *
pspe 0.02827 0.03740 0.75580 0.04834 0.00680 0.819 0.0539 .
amur 0.02647 0.05251 0.50400 0.04512 0.00000 0.853 0.9171
rdie 0.02561 0.09803 0.26120 0.00512 0.04275 0.886 0.5365
ecun 0.02190 0.04456 0.49150 0.03603 0.00000 0.915 0.0420 *
esax 0.01860 0.04544 0.40940 0.01674 0.01687 0.939 0.1259
ptex 0.01585 0.04231 0.37450 0.01170 0.01687 0.959 0.2318
aram 0.01495 0.03676 0.40680 0.01517 0.01261 0.979 0.5894
vros 0.01279 0.03799 0.33650 0.02216 0.00000 0.995 0.8422
ppor 0.00363 0.01891 0.19220 0.00620 0.00000 1.000 0.7063
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Contrast: long_medium
average sd ratio ava avb cumsum p
lgui 0.10221 0.10333 0.98920 0.15918 0.21705 0.133 0.9720
amac 0.10139 0.11774 0.86110 0.07712 0.16122 0.264 0.2078
tnig 0.07029 0.10274 0.68410 0.03804 0.10788 0.356 0.6713
pent 0.06601 0.06862 0.96190 0.10975 0.08112 0.442 0.0260 *
amur 0.05952 0.11624 0.51210 0.04512 0.07283 0.519 0.0649 .
dcor 0.05521 0.09128 0.60480 0.06582 0.03801 0.591 0.8032
ldel 0.04942 0.03935 1.25580 0.08687 0.00185 0.655 0.0010 ***
eul 0.04752 0.07141 0.66540 0.02379 0.07484 0.716 0.9970
htal 0.03907 0.06803 0.57430 0.04599 0.02956 0.767 0.3227
vros 0.03267 0.09018 0.36230 0.02216 0.03599 0.809 0.2198
lwhi 0.02992 0.03771 0.79360 0.04549 0.00840 0.848 0.0010 ***
pspe 0.02952 0.03909 0.75530 0.04834 0.00806 0.887 0.0010 ***
ecun 0.02116 0.04260 0.49670 0.03603 0.00000 0.914 0.0020 **
rdie 0.01844 0.06391 0.28850 0.00512 0.02970 0.938 0.8292
aram 0.01711 0.04409 0.38800 0.01517 0.01739 0.960 0.4705
esax 0.01138 0.02737 0.41600 0.01674 0.00420 0.975 0.6653
ptex 0.00983 0.02516 0.39070 0.01170 0.00658 0.988 0.7073
ppor 0.00929 0.03741 0.24840 0.00620 0.01107 1.000 0.3616
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Contrast: short_medium
average sd ratio ava avb cumsum p
lgui 0.15998 0.16074 0.99530 0.26922 0.21705 0.205 0.0140 *
amac 0.10618 0.14346 0.74010 0.07023 0.16122 0.340 0.1738
eul 0.10520 0.12391 0.84900 0.16793 0.07484 0.475 0.0070 **
tnig 0.08903 0.11469 0.77630 0.07852 0.10788 0.589 0.0799 .
dcor 0.07378 0.14450 0.51060 0.10672 0.03801 0.683 0.2388
pent 0.04966 0.08217 0.60440 0.03392 0.08112 0.747 0.7692
amur 0.04038 0.12310 0.32800 0.00000 0.07283 0.798 0.7073
rdie 0.03751 0.11223 0.33420 0.04275 0.02970 0.847 0.1508
htal 0.03122 0.07878 0.39630 0.02950 0.02956 0.886 0.6993
vros 0.02238 0.09233 0.24240 0.00000 0.03599 0.915 0.6074
aram 0.01559 0.04775 0.32650 0.01261 0.01739 0.935 0.5524
ptex 0.01278 0.04462 0.28650 0.01687 0.00658 0.951 0.4316
esax 0.01161 0.04217 0.27530 0.01687 0.00420 0.966 0.5704
lwhi 0.01095 0.03778 0.28970 0.01261 0.00840 0.980 0.9900
pspe 0.00840 0.02396 0.35050 0.00680 0.00806 0.991 0.9980
ppor 0.00608 0.03495 0.17380 0.00000 0.01107 0.999 0.5385
ldel 0.00101 0.00583 0.17380 0.00000 0.00185 1.000 1.0000
ecun 0.00000 0.00000 NaN 0.00000 0.00000 1.000 0.9990
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Permutation: free
Number of permutations: 1000
Suppose you think of a reptile assemblage as simply the species that
are present, regardless of how common they are. What would you conclude
about the infuence of time since fire now?
Repeat the preceding analysis after creating a new data file that is
presence-absence only.
Run 0 stress 0.1404128
Run 1 stress 0.140413
... Procrustes: rmse 0.000158617 max resid 0.0009441077
... Similar to previous best
Run 2 stress 0.1489204
Run 3 stress 0.1448005
Run 4 stress 0.1486182
Run 5 stress 0.1453965
Run 6 stress 0.1418091
Run 7 stress 0.1415816
Run 8 stress 0.1481748
Run 9 stress 0.1418881
Run 10 stress 0.1404115
... New best solution
... Procrustes: rmse 0.0004234926 max resid 0.002436781
... Similar to previous best
Run 11 stress 0.1488108
Run 12 stress 0.1482426
Run 13 stress 0.1419245
Run 14 stress 0.1590438
Run 15 stress 0.143286
Run 16 stress 0.1486203
Run 17 stress 0.1405587
... Procrustes: rmse 0.01449226 max resid 0.08640004
Run 18 stress 0.1486316
Run 19 stress 0.1405592
... Procrustes: rmse 0.01479786 max resid 0.08730948
Run 20 stress 0.1405595
... Procrustes: rmse 0.01483792 max resid 0.08736059
Run 21 stress 0.1404114
... New best solution
... Procrustes: rmse 0.002731297 max resid 0.02192069
Run 22 stress 0.1496581
Run 23 stress 0.1416846
Run 24 stress 0.1405862
... Procrustes: rmse 0.01597208 max resid 0.09180616
Run 25 stress 0.1461628
Run 26 stress 0.1404123
... Procrustes: rmse 0.000245968 max resid 0.001978068
... Similar to previous best
Run 27 stress 0.1405596
... Procrustes: rmse 0.01457381 max resid 0.08827165
Run 28 stress 0.1404116
... Procrustes: rmse 0.0002275687 max resid 0.001455665
... Similar to previous best
Run 29 stress 0.1478219
Run 30 stress 0.1438487
Run 31 stress 0.1404119
... Procrustes: rmse 0.0001425049 max resid 0.001044504
... Similar to previous best
Run 32 stress 0.1478221
Run 33 stress 0.141641
Run 34 stress 0.1414341
Run 35 stress 0.1422857
Run 36 stress 0.1487658
Run 37 stress 0.1486133
Run 38 stress 0.1502159
Run 39 stress 0.1486756
Run 40 stress 0.1404122
... Procrustes: rmse 0.0002283066 max resid 0.001565205
... Similar to previous best
*** Best solution repeated 4 times

Call:
metaMDS(comm = df1.jac, k = 3, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1.jac
Distance: binary jaccard
Dimensions: 3
Stress: 0.1404114
Stress type 1, weak ties
Best solution was repeated 4 times in 40 tries
The best solution was from try 21 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Run 0 stress 0.2009509
Run 1 stress 0.2019149
Run 2 stress 0.2011657
... Procrustes: rmse 0.006416695 max resid 0.0398645
Run 3 stress 0.202576
Run 4 stress 0.2284835
Run 5 stress 0.2197434
Run 6 stress 0.2011646
... Procrustes: rmse 0.006850207 max resid 0.03839815
Run 7 stress 0.2204112
Run 8 stress 0.215058
Run 9 stress 0.203002
Run 10 stress 0.2143484
Run 11 stress 0.2104918
Run 12 stress 0.2180894
Run 13 stress 0.2279185
Run 14 stress 0.2071546
Run 15 stress 0.2160939
Run 16 stress 0.2164477
Run 17 stress 0.2108417
Run 18 stress 0.2097709
Run 19 stress 0.2079378
Run 20 stress 0.2138375
Run 21 stress 0.2120034
Run 22 stress 0.2115225
Run 23 stress 0.215718
Run 24 stress 0.2057211
Run 25 stress 0.2030018
Run 26 stress 0.213385
Run 27 stress 0.2285741
Run 28 stress 0.2289543
Run 29 stress 0.2178744
Run 30 stress 0.208991
Run 31 stress 0.2135402
Run 32 stress 0.20361
Run 33 stress 0.2156126
Run 34 stress 0.2146268
Run 35 stress 0.2167606
Run 36 stress 0.2274825
Run 37 stress 0.202578
Run 38 stress 0.2036086
Run 39 stress 0.2171294
Run 40 stress 0.2366921
Run 41 stress 0.2011785
... Procrustes: rmse 0.006149074 max resid 0.03876166
Run 42 stress 0.218512
Run 43 stress 0.2020987
Run 44 stress 0.2068717
Run 45 stress 0.2041772
Run 46 stress 0.203832
Run 47 stress 0.2272148
Run 48 stress 0.2035363
Run 49 stress 0.2074059
Run 50 stress 0.2174067
Run 51 stress 0.2098787
Run 52 stress 0.2074132
Run 53 stress 0.2011648
... Procrustes: rmse 0.006869384 max resid 0.03837032
Run 54 stress 0.2133796
Run 55 stress 0.2139331
Run 56 stress 0.2112664
Run 57 stress 0.226952
Run 58 stress 0.2011782
... Procrustes: rmse 0.006123098 max resid 0.03888408
Run 59 stress 0.2119751
Run 60 stress 0.2133246
Run 61 stress 0.2134668
Run 62 stress 0.2045553
Run 63 stress 0.2084428
Run 64 stress 0.2019056
Run 65 stress 0.2041934
Run 66 stress 0.2144476
Run 67 stress 0.2068721
Run 68 stress 0.2128513
Run 69 stress 0.2069873
Run 70 stress 0.2116038
Run 71 stress 0.2187148
Run 72 stress 0.2030068
Run 73 stress 0.2078151
Run 74 stress 0.2011768
... Procrustes: rmse 0.005962949 max resid 0.03913871
Run 75 stress 0.2056871
Run 76 stress 0.2011778
... Procrustes: rmse 0.006066117 max resid 0.03889517
Run 77 stress 0.2177676
Run 78 stress 0.2127882
Run 79 stress 0.2111792
Run 80 stress 0.2014982
*** Best solution was not repeated -- monoMDS stopping criteria:
12: no. of iterations >= maxit
68: stress ratio > sratmax

Call:
metaMDS(comm = df1.jac, k = 2, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1.jac
Distance: binary jaccard
Dimensions: 2
Stress: 0.2009509
Stress type 1, weak ties
Best solution was not repeated after 80 tries
The best solution was from try 0 (metric scaling or null solution)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Marginal decision here - stress just over 0.2 for k=2, so might be
OK. Stress good for k=3, but 2-d MDS usually better for reporting or
showing to audience

Unburned sites separate very clearly on MDS1. Pattern clearer than
with abundances included
Do permanova including tsf
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
adonis2(formula = df1.jac ~ tsf, data = df, permutations = 999)
Df SumOfSqs R2 F Pr(>F)
tsf 2 3.7853 0.20678 9.9057 0.001 ***
Residual 76 14.5210 0.79322
Total 78 18.3062 1.00000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Clear fire signal
Extension activity
Dixon and her colleagues also recorded a range of habitat variables,
which we’ve collected for you in dixonenv.csv
Rows: 79 Columns: 14── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (4): site, tsf, veg, aspect
dbl (10): lcwd, shrcov, grcov, litcov, litdep, rocks, elev, warm, cold, twi
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
They recorded Coarse Woody Debris, which was long-transformed, litter
cover (litcov), % cover of groundcover (grcov), and % cover of shrubs
(shrcov), and rock cover. In the original paper, Dixon et al. were
comfortable that these predictors weren’t correlated.
mvabund
Error in model.frame.default(formula = dfmv ~ dixonenv$tsf + dixonenv$lcwd + :
variable lengths differ (found for 'dixonenv$tsf')
B Simple MDS & Permanova
Let’s return to the Hutto and Barrett
(2021) example from the Chapter 15 exercises. There, we used
similarity-based analyses to explore the relationship between frog
assemblages in ponds and the degree of urbanization surrounding. This
seems a question that could just as easily be examined using distances
or dissimilarities.
Return to the data and assess whether frog assemblages (using the
standardized abundance scale or presence-absence) differ with
urbanization.
Did your conclusions differ from those obtained using RDA?
Rows: 50 Columns: 14── Column specification ──────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): type
dbl (13): Site, ACRE, BAME, BFOW, GCAR, HCIN, HVER, LCAT, LCLA, LPAL, LSPH, PCRU, PFER
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
The explanation of the variables is in the previous chapter’s
exercises.
Run 0 stress 0.196708
Run 1 stress 0.1877627
... New best solution
... Procrustes: rmse 0.06210972 max resid 0.2289889
Run 2 stress 0.1965252
Run 3 stress 0.2177645
Run 4 stress 0.1983645
Run 5 stress 0.2034451
Run 6 stress 0.2052112
Run 7 stress 0.1877626
... New best solution
... Procrustes: rmse 0.0001156879 max resid 0.0003505044
... Similar to previous best
Run 8 stress 0.185584
... New best solution
... Procrustes: rmse 0.07743106 max resid 0.5021775
Run 9 stress 0.1992463
Run 10 stress 0.1974204
Run 11 stress 0.1946875
Run 12 stress 0.1862779
Run 13 stress 0.1863292
Run 14 stress 0.2005585
Run 15 stress 0.1920873
Run 16 stress 0.1875597
Run 17 stress 0.1964527
Run 18 stress 0.1920872
Run 19 stress 0.1977907
Run 20 stress 0.2167665
Run 21 stress 0.1875595
Run 22 stress 0.1929107
Run 23 stress 0.1975661
Run 24 stress 0.186278
Run 25 stress 0.1875598
Run 26 stress 0.1960212
Run 27 stress 0.1991282
Run 28 stress 0.1975497
Run 29 stress 0.185397
... New best solution
... Procrustes: rmse 0.02114207 max resid 0.1079972
Run 30 stress 0.1969418
Run 31 stress 0.186278
Run 32 stress 0.1862238
Run 33 stress 0.1877806
Run 34 stress 0.1919384
Run 35 stress 0.1967647
Run 36 stress 0.2073798
Run 37 stress 0.1888207
Run 38 stress 0.2054248
Run 39 stress 0.1874611
Run 40 stress 0.1862237
Run 41 stress 0.186278
Run 42 stress 0.1888251
Run 43 stress 0.1937375
Run 44 stress 0.1862237
Run 45 stress 0.1963067
Run 46 stress 0.1862237
Run 47 stress 0.1854373
... Procrustes: rmse 0.009296219 max resid 0.0491063
Run 48 stress 0.1920872
Run 49 stress 0.1875595
Run 50 stress 0.1853641
... New best solution
... Procrustes: rmse 0.001953553 max resid 0.00909663
... Similar to previous best
*** Best solution repeated 1 times

Call:
metaMDS(comm = df1.bc, k = 2, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1.bc
Distance: bray
Dimensions: 2
Stress: 0.1853641
Stress type 1, weak ties
Best solution was repeated 1 time in 50 tries
The best solution was from try 50 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Run 0 stress 0.129187
Run 1 stress 0.1291859
... New best solution
... Procrustes: rmse 0.0008388266 max resid 0.00496375
... Similar to previous best
Run 2 stress 0.1402078
Run 3 stress 0.1308799
Run 4 stress 0.1289613
... New best solution
... Procrustes: rmse 0.01088561 max resid 0.05621761
Run 5 stress 0.129186
... Procrustes: rmse 0.01089164 max resid 0.05582815
Run 6 stress 0.1289616
... Procrustes: rmse 0.0002674815 max resid 0.001155959
... Similar to previous best
Run 7 stress 0.1380881
Run 8 stress 0.1425061
Run 9 stress 0.1395557
Run 10 stress 0.1291859
... Procrustes: rmse 0.01090439 max resid 0.05603889
Run 11 stress 0.1291861
... Procrustes: rmse 0.01047698 max resid 0.0544579
Run 12 stress 0.1380864
Run 13 stress 0.12921
... Procrustes: rmse 0.01243608 max resid 0.06398953
Run 14 stress 0.1291867
... Procrustes: rmse 0.01108112 max resid 0.05658361
Run 15 stress 0.1380875
Run 16 stress 0.1289612
... New best solution
... Procrustes: rmse 0.0001897893 max resid 0.001008599
... Similar to previous best
Run 17 stress 0.1291861
... Procrustes: rmse 0.01047209 max resid 0.05451001
Run 18 stress 0.1384298
Run 19 stress 0.1291858
... Procrustes: rmse 0.01085358 max resid 0.05610837
Run 20 stress 0.1289617
... Procrustes: rmse 0.0005107488 max resid 0.002356854
... Similar to previous best
Run 21 stress 0.129192
... Procrustes: rmse 0.01049379 max resid 0.05482609
Run 22 stress 0.1291861
... Procrustes: rmse 0.01090769 max resid 0.05651704
Run 23 stress 0.1291858
... Procrustes: rmse 0.01084092 max resid 0.05603118
Run 24 stress 0.1291603
... Procrustes: rmse 0.009742854 max resid 0.05179386
Run 25 stress 0.1291861
... Procrustes: rmse 0.01048144 max resid 0.05456092
Run 26 stress 0.1291857
... Procrustes: rmse 0.01077451 max resid 0.05553841
Run 27 stress 0.1380876
Run 28 stress 0.1402635
Run 29 stress 0.1384275
Run 30 stress 0.1291864
... Procrustes: rmse 0.01045087 max resid 0.05448513
Run 31 stress 0.129186
... Procrustes: rmse 0.01090378 max resid 0.0564044
Run 32 stress 0.1291859
... Procrustes: rmse 0.01083027 max resid 0.0561575
Run 33 stress 0.1380913
Run 34 stress 0.1291855
... Procrustes: rmse 0.01069769 max resid 0.05541034
Run 35 stress 0.1383999
Run 36 stress 0.1289618
... Procrustes: rmse 0.0005305334 max resid 0.002504772
... Similar to previous best
Run 37 stress 0.1291859
... Procrustes: rmse 0.01084244 max resid 0.05590108
Run 38 stress 0.1289621
... Procrustes: rmse 0.0006163776 max resid 0.002721091
... Similar to previous best
Run 39 stress 0.1291858
... Procrustes: rmse 0.01057936 max resid 0.05497957
Run 40 stress 0.1291858
... Procrustes: rmse 0.01050048 max resid 0.05461872
*** Best solution repeated 4 times

Call:
metaMDS(comm = df1.bc, k = 3, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1.bc
Distance: bray
Dimensions: 3
Stress: 0.1289612
Stress type 1, weak ties
Best solution was repeated 4 times in 40 tries
The best solution was from try 16 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
2-d is acceptable

Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
adonis2(formula = df1.bc ~ type, data = df, permutations = 999)
Df SumOfSqs R2 F Pr(>F)
type 2 0.912 0.07281 1.7669 0.034 *
Residual 45 11.614 0.92719
Total 47 12.526 1.00000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Permanova detects a difference; MDS plot suggests low urbanization
may be different from the other two, though worth looking at dispersion
as well, as spread of this type is less than the other two on plot
Repeat analysis with presence-absence
df1.jac <- vegdist(df1,binary=TRUE,method=‘jaccard’)
Run 0 stress 0.1551612
Run 1 stress 0.1538244
... New best solution
... Procrustes: rmse 0.01653307 max resid 0.06524188
Run 2 stress 0.1808491
Run 3 stress 0.1646706
Run 4 stress 0.1901198
Run 5 stress 0.1908161
Run 6 stress 0.1607835
Run 7 stress 0.1961593
Run 8 stress 0.163888
Run 9 stress 0.158713
Run 10 stress 0.1551611
Run 11 stress 0.1728782
Run 12 stress 0.1627091
Run 13 stress 0.1602264
Run 14 stress 0.1538803
... Procrustes: rmse 0.0179707 max resid 0.07573361
Run 15 stress 0.1609335
Run 16 stress 0.1646707
Run 17 stress 0.1945193
Run 18 stress 0.1837141
Run 19 stress 0.1669303
Run 20 stress 0.1585798
Run 21 stress 0.1630282
Run 22 stress 0.15858
Run 23 stress 0.1585799
Run 24 stress 0.1734741
Run 25 stress 0.1630923
Run 26 stress 0.1585799
Run 27 stress 0.1602583
Run 28 stress 0.15858
Run 29 stress 0.1752544
Run 30 stress 0.1784224
Run 31 stress 0.1609031
Run 32 stress 0.1553998
Run 33 stress 0.1707427
Run 34 stress 0.1604495
Run 35 stress 0.1623918
Run 36 stress 0.1646706
Run 37 stress 0.1781197
Run 38 stress 0.1622267
Run 39 stress 0.1669302
Run 40 stress 0.1629465
Run 41 stress 0.1627091
Run 42 stress 0.1760835
Run 43 stress 0.1538804
... Procrustes: rmse 0.01791116 max resid 0.07567211
Run 44 stress 0.1603052
Run 45 stress 0.1666163
Run 46 stress 0.1538248
... Procrustes: rmse 0.0003646799 max resid 0.001890428
... Similar to previous best
*** Best solution repeated 1 times

Call:
metaMDS(comm = df1.jac, k = 2, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1.jac
Distance: binary jaccard
Dimensions: 2
Stress: 0.1538244
Stress type 1, weak ties
Best solution was repeated 1 time in 46 tries
The best solution was from try 1 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Run 0 stress 0.09466813
Run 1 stress 0.09466799
... New best solution
... Procrustes: rmse 0.0005113888 max resid 0.002601587
... Similar to previous best
Run 2 stress 0.1116796
Run 3 stress 0.09466791
... New best solution
... Procrustes: rmse 5.140713e-05 max resid 0.0001769429
... Similar to previous best
Run 4 stress 0.09466788
... New best solution
... Procrustes: rmse 6.431395e-05 max resid 0.0002594411
... Similar to previous best
Run 5 stress 0.09466814
... Procrustes: rmse 0.0001741567 max resid 0.0005987574
... Similar to previous best
Run 6 stress 0.109059
Run 7 stress 0.09466798
... Procrustes: rmse 8.15394e-05 max resid 0.0003917043
... Similar to previous best
Run 8 stress 0.09466792
... Procrustes: rmse 8.950007e-05 max resid 0.0003379089
... Similar to previous best
Run 9 stress 0.09466804
... Procrustes: rmse 0.0001189413 max resid 0.0003712925
... Similar to previous best
Run 10 stress 0.1004901
Run 11 stress 0.09466837
... Procrustes: rmse 0.0002451238 max resid 0.001009793
... Similar to previous best
Run 12 stress 0.09694634
Run 13 stress 0.09466805
... Procrustes: rmse 0.0001311181 max resid 0.0006621851
... Similar to previous best
Run 14 stress 0.09466838
... Procrustes: rmse 0.0002467991 max resid 0.00110516
... Similar to previous best
Run 15 stress 0.1097138
Run 16 stress 0.09466796
... Procrustes: rmse 0.0001191739 max resid 0.0005138992
... Similar to previous best
Run 17 stress 0.09466843
... Procrustes: rmse 0.0005603326 max resid 0.002919388
... Similar to previous best
Run 18 stress 0.1005045
Run 19 stress 0.09466785
... New best solution
... Procrustes: rmse 4.336385e-05 max resid 0.0001341018
... Similar to previous best
Run 20 stress 0.09466823
... Procrustes: rmse 0.0004406253 max resid 0.00239166
... Similar to previous best
Run 21 stress 0.09466821
... Procrustes: rmse 0.0002307082 max resid 0.0007713212
... Similar to previous best
Run 22 stress 0.09693811
Run 23 stress 0.09466805
... Procrustes: rmse 0.0001145164 max resid 0.0005228285
... Similar to previous best
Run 24 stress 0.09466802
... Procrustes: rmse 0.0001210626 max resid 0.0004425707
... Similar to previous best
Run 25 stress 0.1005046
Run 26 stress 0.09466798
... Procrustes: rmse 0.000102713 max resid 0.0004059971
... Similar to previous best
Run 27 stress 0.09466796
... Procrustes: rmse 8.304787e-05 max resid 0.000343865
... Similar to previous best
Run 28 stress 0.1090607
Run 29 stress 0.1097141
Run 30 stress 0.1131481
Run 31 stress 0.09693847
Run 32 stress 0.1131483
Run 33 stress 0.09466825
... Procrustes: rmse 0.0002105948 max resid 0.0008409997
... Similar to previous best
Run 34 stress 0.1116801
Run 35 stress 0.09466791
... Procrustes: rmse 0.0001849118 max resid 0.0006962707
... Similar to previous best
Run 36 stress 0.09466793
... Procrustes: rmse 0.0001164267 max resid 0.0003992448
... Similar to previous best
Run 37 stress 0.09693871
Run 38 stress 0.09466835
... Procrustes: rmse 0.0002585436 max resid 0.001174372
... Similar to previous best
Run 39 stress 0.1005044
Run 40 stress 0.09693812
*** Best solution repeated 11 times

Call:
metaMDS(comm = df1.jac, k = 3, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1.jac
Distance: binary jaccard
Dimensions: 3
Stress: 0.09466785
Stress type 1, weak ties
Best solution was repeated 11 times in 40 tries
The best solution was from try 19 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Again, stress OK with 2D, good with 3D. Look at 2D first

Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
adonis2(formula = df1.jac ~ type, data = df, permutations = 999)
Df SumOfSqs R2 F Pr(>F)
type 2 0.4525 0.04389 1.0328 0.404
Residual 45 9.8587 0.95611
Total 47 10.3112 1.00000
No separation seen on Presence-Absence
C
Griffen et al. (2019) examined the oral
microbiome of humans, with a focus on the effects of HIV and
AntiRetroviral therapy (ART) on this microbiome. They described the
microbiome of 341 patients, who fell into one of two categories:
HIV-, and HIV+ with ART. They also matched their samples as
far as possible for sex, along with other conditions that can influence
oral microbiomes (Candida infection, current smoking). We’ll
use their records for these other categories as well. There were more
HIV+ than - subjects, but within these groups, approximately equal
numbers of two sexes, two Candida infection status, and two
smoking categories.
The bacteriome was recorded separately using 16S RNA sequencing,
which overed just over 600 taxa.
The data are available from their paper, as two Excel files in the
supplementary information. The metadata gives HIV status, and a raft of
demographic information. We’ll just work with HIV, sex,
Candida, and current smoking. A second sheet has the
bacteriome. The code chunk below reads this file (from a Downloads
folder - you’ll need to modify the file location). It also screens the
file for any bacterial taxa that were not present in this particular
study, which reduces the bacterial taxa to 599.
New names:
Use a dissimilarity based approach to assess the combined effects of
HIV-ART, sex, Candida infection, and current smoking on the
bacteriome
Do these factors act independently on the
bacteriome?
Which effects are largest (use some graphical
methods)?
First steps: Think about standardization and which
distance measure you’ll use. Bray-Curtis seems common for these kind of
data, and and counts of different taxa vary widely.
Run factorial model using permanova, based on B-C
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
adonis2(formula = df1s.bc ~ HIV * candida * gender * smoking_current, data = df, permutations = 999)
Df SumOfSqs R2 F Pr(>F)
HIV 1 1.369 0.01250 4.3776 0.001 ***
candida 1 1.461 0.01333 4.6694 0.001 ***
gender 1 0.492 0.00449 1.5737 0.016 *
smoking_current 1 1.111 0.01014 3.5513 0.001 ***
HIV:candida 1 0.318 0.00290 1.0151 0.375
HIV:gender 1 0.354 0.00324 1.1332 0.214
candida:gender 1 0.257 0.00234 0.8202 0.830
HIV:smoking_current 1 0.269 0.00245 0.8584 0.773
candida:smoking_current 1 0.344 0.00314 1.0989 0.250
gender:smoking_current 1 0.394 0.00360 1.2602 0.096 .
HIV:candida:gender 1 0.349 0.00319 1.1164 0.235
HIV:candida:smoking_current 1 0.280 0.00255 0.8943 0.679
HIV:gender:smoking_current 1 0.265 0.00242 0.8463 0.784
candida:gender:smoking_current 1 0.254 0.00232 0.8110 0.873
HIV:candida:gender:smoking_current 1 0.362 0.00330 1.1562 0.198
Residual 325 101.664 0.92809
Total 340 109.541 1.00000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Model shows main effects, but no interactions important (or at least,
detected)
Could you fit a simpler model to the data?
Run simpler model
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
adonis2(formula = df1s.bc ~ HIV + candida + gender + smoking_current, data = df, permutations = 999)
Df SumOfSqs R2 F Pr(>F)
HIV 1 1.369 0.01250 4.3775 0.001 ***
candida 1 1.461 0.01333 4.6693 0.001 ***
gender 1 0.492 0.00449 1.5736 0.009 **
smoking_current 1 1.111 0.01014 3.5512 0.001 ***
Residual 336 105.108 0.95953
Total 340 109.541 1.00000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
No change; not too surprising, as all four main effects were detected
easily.
Now go to data visualization
Run 0 stress 0.1573956
Run 1 stress 0.1575191
... Procrustes: rmse 0.008589029 max resid 0.09901144
Run 2 stress 0.1578788
... Procrustes: rmse 0.01041235 max resid 0.1078867
Run 3 stress 0.157925
Run 4 stress 0.1575481
... Procrustes: rmse 0.01188138 max resid 0.1520687
Run 5 stress 0.1579133
Run 6 stress 0.1576591
... Procrustes: rmse 0.009942152 max resid 0.1527314
Run 7 stress 0.157497
... Procrustes: rmse 0.01111373 max resid 0.1522922
Run 8 stress 0.1579538
Run 9 stress 0.1576133
... Procrustes: rmse 0.01189532 max resid 0.1519556
Run 10 stress 0.1577343
... Procrustes: rmse 0.005452067 max resid 0.07804308
Run 11 stress 0.1578963
Run 12 stress 0.1579279
Run 13 stress 0.1576016
... Procrustes: rmse 0.0109762 max resid 0.107016
Run 14 stress 0.1579049
Run 15 stress 0.1589585
Run 16 stress 0.1578044
... Procrustes: rmse 0.01067844 max resid 0.1064934
Run 17 stress 0.1579047
Run 18 stress 0.158098
Run 19 stress 0.1572868
... New best solution
... Procrustes: rmse 0.008393785 max resid 0.1530693
Run 20 stress 0.1575303
... Procrustes: rmse 0.007358023 max resid 0.09985515
Run 21 stress 0.1590169
Run 22 stress 0.1574836
... Procrustes: rmse 0.007062616 max resid 0.09973642
Run 23 stress 0.1589497
Run 24 stress 0.1575418
... Procrustes: rmse 0.01043605 max resid 0.1071247
Run 25 stress 0.1575948
... Procrustes: rmse 0.007994064 max resid 0.100641
Run 26 stress 0.1589119
Run 27 stress 0.157732
... Procrustes: rmse 0.01101245 max resid 0.1526594
Run 28 stress 0.157637
... Procrustes: rmse 0.009312799 max resid 0.1014359
Run 29 stress 0.1578533
Run 30 stress 0.1580676
Run 31 stress 0.1576151
... Procrustes: rmse 0.009459453 max resid 0.152878
Run 32 stress 0.1577917
Run 33 stress 0.157414
... Procrustes: rmse 0.006382718 max resid 0.09822517
Run 34 stress 0.1576762
... Procrustes: rmse 0.01303633 max resid 0.1519725
Run 35 stress 0.158515
Run 36 stress 0.1591759
Run 37 stress 0.1581336
Run 38 stress 0.1576021
... Procrustes: rmse 0.004976543 max resid 0.08068629
Run 39 stress 0.157918
Run 40 stress 0.1579179
Run 41 stress 0.1579341
Run 42 stress 0.1582696
Run 43 stress 0.157666
... Procrustes: rmse 0.00894034 max resid 0.1018467
Run 44 stress 0.157331
... Procrustes: rmse 0.005409824 max resid 0.09767552
Run 45 stress 0.1577833
... Procrustes: rmse 0.006683058 max resid 0.08363389
Run 46 stress 0.1575939
... Procrustes: rmse 0.008116432 max resid 0.1084878
Run 47 stress 0.1575258
... Procrustes: rmse 0.01301618 max resid 0.1519787
Run 48 stress 0.1592999
Run 49 stress 0.1579052
Run 50 stress 0.1576273
... Procrustes: rmse 0.01129313 max resid 0.1523282
Run 51 stress 0.1578542
Run 52 stress 0.1586214
Run 53 stress 0.1581151
Run 54 stress 0.1575617
... Procrustes: rmse 0.004502256 max resid 0.07990366
Run 55 stress 0.158704
Run 56 stress 0.1580142
Run 57 stress 0.1579508
Run 58 stress 0.1572867
... New best solution
... Procrustes: rmse 0.0001807269 max resid 0.002841007
... Similar to previous best
*** Best solution repeated 1 times

Call:
metaMDS(comm = df1s.bc, k = 3, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1s.bc
Distance: bray
Dimensions: 3
Stress: 0.1572867
Stress type 1, weak ties
Best solution was repeated 1 time in 58 tries
The best solution was from try 58 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
Run 0 stress 0.2249552
Run 1 stress 0.2254015
... Procrustes: rmse 0.01352051 max resid 0.2271372
Run 2 stress 0.2255455
Run 3 stress 0.2258301
Run 4 stress 0.2253491
... Procrustes: rmse 0.01645725 max resid 0.2296993
Run 5 stress 0.22481
... New best solution
... Procrustes: rmse 0.006257423 max resid 0.08115346
Run 6 stress 0.226546
Run 7 stress 0.2270536
Run 8 stress 0.2255036
Run 9 stress 0.2253569
Run 10 stress 0.2248483
... Procrustes: rmse 0.004470422 max resid 0.08182654
Run 11 stress 0.2471961
Run 12 stress 0.2258085
Run 13 stress 0.2323029
Run 14 stress 0.2248951
... Procrustes: rmse 0.004402054 max resid 0.08037907
Run 15 stress 0.2251572
... Procrustes: rmse 0.01045667 max resid 0.1510096
Run 16 stress 0.2253558
Run 17 stress 0.2254108
Run 18 stress 0.2250959
... Procrustes: rmse 0.009892968 max resid 0.1562671
Run 19 stress 0.225423
Run 20 stress 0.2248147
... Procrustes: rmse 0.0005021359 max resid 0.007253184
... Similar to previous best
Run 21 stress 0.2253845
Run 22 stress 0.224894
... Procrustes: rmse 0.004397181 max resid 0.08032982
Run 23 stress 0.2255606
Run 24 stress 0.2260425
Run 25 stress 0.2261645
Run 26 stress 0.2253466
Run 27 stress 0.2277116
Run 28 stress 0.2255894
Run 29 stress 0.2250862
... Procrustes: rmse 0.009777865 max resid 0.1540782
Run 30 stress 0.2257552
Run 31 stress 0.2253727
Run 32 stress 0.225797
Run 33 stress 0.2248478
... Procrustes: rmse 0.004466226 max resid 0.08183205
Run 34 stress 0.2250846
... Procrustes: rmse 0.009723839 max resid 0.1530552
Run 35 stress 0.2258302
Run 36 stress 0.2257291
Run 37 stress 0.22485
... Procrustes: rmse 0.004479105 max resid 0.08182191
Run 38 stress 0.2255518
Run 39 stress 0.2253414
Run 40 stress 0.2256079
*** Best solution repeated 1 times

Call:
metaMDS(comm = df1s.bc, k = 2, try = 40, trymax = 80, autotransform = FALSE, maxit = 200)
global Multidimensional Scaling using monoMDS
Data: df1s.bc
Distance: bray
Dimensions: 2
Stress: 0.22481
Stress type 1, weak ties
Best solution was repeated 1 time in 40 tries
The best solution was from try 5 (random start)
Scaling: centring, PC rotation, halfchange scaling
Species: scores missing
3D model fits better than 2D. Stress for 2D above 0.2
Start with plots where symbol colour indicates levels of one of the
factors




Try some visualizations of pairs of factors using MDS1 & MDS2
(while 3D is preferred, stress of 3D is around .15, vs 0.22, so not huge
difference) Separate HIV+/-, then use symbol colour to separate second
factor.



References
Dixon, Kelly M., Geoffrey J. Cary, Graeme L. Worboys, and Philip
Gibbons. 2018.
“The Disproportionate Importance of Long‐unburned
Forests and Woodlands for Reptiles.” Ecology and
Evolution 8 (22): 10952–63.
https://doi.org/gfs587.
Griffen, Ann L., Zachary A. Thompson, Clifford J. Beall, Elizabeth A.
Lilly, Carolina Granada, Kelly D. Treas, Kenneth R. DuBois, et al. 2019.
“Significant Effect of HIV/HAART on Oral
Microbiota Using Multivariate Analysis.” Scientific
Reports 9 (1): 19946.
https://doi.org/gsfpz3.
Hutto, David, and Kyle Barrett. 2021.
“Do Urban Open Spaces
Provide Refugia for Frogs in Urban Environments?” Plos
One 16 (1).
https://doi.org/gr2r9n.
---
title: "Ch 16 exercises"
output: 
  html_notebook:
    theme: flatly
bibliography: ../web_ex.bib
---

```{r echo=FALSE, results='hide'}
# Packages: vegan,mvabund
source("../R/libraries.R")
source("../R/appearance.R")
library(vegan)
library(mvabund)
```

The aim of these exercises is to continue making sure you're comfortable with handling multivariate data. In this chapter's, you'll focus on analyses based on dissimilarities/distances, including fitting linear models to these kinds of response variables.

For each of the examples below, you should follow the sequence we've used previously, as far as it's sensible:

1.  What is the biological question?

2.  Is the predictor continuous or categorical?

3.  Write out the linear model corresponding to this question.

4.  What distribution do you expect the response variable to follow?

5.  What are the assumptions behind the statistical model you'll fit?

    1.  Are those assumptions satisfied?

6.  Fit the model

    1.  How will you assess whether the model fits well?

    2.  Can you detect an effect of the predictors?

    3.  How do you measure the effect?

7.  What do you conclude (including any cautions)

------------------------------------------------------------------------

## A

@dixonDisproportionateImportanceLong2018 focused on assemblages of reptiles in forests and woodlands of southeastern Australia, with a particular interest in relationships between these assemblages and the fire history of the landscape. They identified 81 sites that varied in time since fire, from 6 months to \>96 y. Rather than a continuum, three categories of time since fire were used, 0.5-2y, 6-12y, and \>96y. Sites were also classified according to habitat.

Reptile assemblages were sampled with a range of methods, including visual surveys and camera traps, to give counts of 20 reptiles, whose abundance ranged from 0-1 to 0-126, depending on species.

Data are available from [dryad](https://datadryad.org/stash/dataset/doi:10.5061/dryad.gh5m471), as Rep_abund.csv. You'll want to focus on the columns with reptile numbers, and the one with the fire history (tsf). For convenience, we've extracted those data as dixonbiota.csv

**Start by having a quick look at the data.**

```{r}
df <- read_csv("../data/dixonbiota.csv")
head(df, 10)
```

The file is pretty straightforward, with tsf being the fire category, and columns 3-22 each representing one reptile taxon.

## Outline how you'd assess whether the reptile assemblage (the combination of species present and their abundances) is related to fire history, using a dissimilarity-based approach.

You should think about how you'll deal with the data:

-   Will you need a transformation, standardization, etc.?

-   What are the consequences of any decisions you make for the interpretation of your analysis?

-   What measure(s) of dissimilarity are appropriate?

### Run the analysis and provide your interpretation

> ### MDS on reptile abundances

> Start with dissimilarities
>
> Students should have some discussion of raw vs transformed (e.g. 4th root), standardization.
>
> Fourth root is common. Using it downweights the influence of abundant species, while raw allows those species to have a strong influence. There are questions about which one of these reflects ecological function better
>
> Data are all abundances

```{r}
df1 <- df[,-(1:2)]   #Stripped back file without labels, leaving only 
df1s <- wisconsin(df1)   #Common to do some standardisation
df1s.bc <- vegdist(df1s,'bray')   #With standardisation (wisconsin)
```

> Visualize results

> Need to decide whether to use 2 or 3 dimensions

```{r}
#Run 3d first
df1s.mds3 <- metaMDS(df1s.bc,k=3,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1s.mds3, main="Shepard plot")
df1s.mds3
# Now look at 2d
df1s.mds2 <- metaMDS(df1s.bc,k=2,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1s.mds2, main="Shepard plot")
df1s.mds2
```

> Stress values suggest 3d plot is a more accurate representation

> Need to plot dim 1 vs dim 2 and dim 1 vs dim 3 with tsf groups identified by symbols
>
> **Generate graphs**
>
> This is a variant of code used in worked example for Ch 16. It does use the graph settings defined in *appearance.R*, which is called earlier.

```{r}
a<-as.data.frame(scores(df1s.mds3))
a<-cbind(df[c(1:2)],a)   #Add site names & symbols from original data file
p1<-ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=tsf, ) )+
  geom_point()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=sym3,
                     name="TSF",
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=a, aes(x=NMDS1, y=NMDS3, color = tsf, ) )+
  geom_point()+
  labs(y="MDS3", x="MDS1")+
  scale_shape_manual(values=sym3,
                     name="TSF",
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )

p1 + p2 + plot_layout(guides='collect') & theme_qk() & scale_color_uchicago()
```

### How would you fit a linear model to assess fire effects?

> Do permanova including tsf

```{r}
df1s.ado <- adonis2(df1s.bc~tsf,data=df,permutations=999)
print(df1s.ado)
```

> Permanova suggests strong signal from tsf

> SIMPER analysis for tsf group differences

```{r}
df.sim <- simper(df1s[,-(1:2)], df$tsf, permutations=1000)
summary(df.sim)
```

## Suppose you think of a reptile assemblage as simply the species that are present, regardless of how common they are. What would you conclude about the infuence of time since fire now?

> Repeat the preceding analysis after creating a new data file that is presence-absence only.

```{r}
df1.jac <- vegdist(df1,binary=TRUE,method='jaccard')
#Run 3d first
df1s.mds3 <- metaMDS(df1.jac,k=3,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1s.mds3, main="Shepard plot")
df1s.mds3
# Now look at 2d
df1s.mds2 <- metaMDS(df1.jac,k=2,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1s.mds2, main="Shepard plot")
df1s.mds2
```

> Marginal decision here - stress just over 0.2 for k=2, so might be OK. Stress good for k=3, but 2-d MDS usually better for reporting or showing to audience

```{r}
a<-as.data.frame(scores(df1s.mds3))
a<-cbind(df[c(1:2)],a)   #Add site names & symbols from original data file
p1<-ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=tsf, ) )+
  geom_point()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=sym3,
                     name="TSF",
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=a, aes(x=NMDS1, y=NMDS3, color = tsf, ) )+
  geom_point()+
  labs(y="MDS3", x="MDS1")+
  scale_shape_manual(values=sym3,
                     name="TSF",
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )

p1 + p2 + plot_layout(guides='collect') & theme_qk() & scale_color_uchicago()
```

> Unburned sites separate very clearly on MDS1. Pattern clearer than with abundances included

> Do permanova including tsf

```{r}
df1.ado <- adonis2(df1.jac~tsf,data=df,permutations=999)
print(df1.ado)
```

> Clear fire signal

## Extension activity

Dixon and her colleagues also recorded a range of habitat variables, which we've collected for you in dixonenv.csv

```{r}
dixonenv <- read_csv("../data/dixonenv.csv")
head(dixonenv, 10)
```

They recorded Coarse Woody Debris, which was long-transformed, litter cover (litcov), % cover of groundcover (grcov), and % cover of shrubs (shrcov), and rock cover. In the original paper, Dixon et al. were comfortable that these predictors weren't correlated.

### How is reptile assemblage related to time since fire and these five habitat variables

> Check continuous predictors

```{r}
boxplot(dixonenv$lcwd)
boxplot(dixonenv$litcov)
boxplot(dixonenv$grcov)
boxplot(dixonenv$shrcov)
boxplot(dixonenv$rocks)
#transform rocks to log+1
dixonenv$lrocks <- log10(dixonenv$rocks+1)
# check homog of dispersions on double standardized abundances
df1s.disp <- betadisper(df1s.bc,df$tsf)
anova(df1s.disp)
```

> do permanova including tsf plus continuous predictors

```{r}
df1s.ado <- adonis2(df1s.bc~tsf+lcwd+litcov+grcov+shrcov+lrocks,data=dixonenv,permutations=999)
print(df1s.ado)
#Run analysis for presence-absence as well
df1.jac.ado <- adonis2(df1.jac~tsf+lcwd+litcov+grcov+shrcov+lrocks,data=dixonenv,permutations=999)
print(df1.jac.ado)

```

> Main effect is tsf; only some question about CWD when we look at species composition and abundance, while for presence-absence data, there are also effects of CWD and groundcover

### mvabund

```{r error=TRUE}
dfmv <- mvabund(df[,-(1:2)])
dfmv.mv <- manyglm(dfmv~dixonenv$tsf+dixonenv$lcwd+dixonenv$litcov+dixonenv$grcov+dixonenv$shrcov+dixonenv$lrocks,family="poisson")
plot(dixonbiotamv.mv)
# still hetero vars so use -ve binomial
dfmv1.mv <- manyglm(dfmv~dixonenv$tsf+dixonenv$lcwd+dixonenv$litcov+dixonenv$grcov+dixonenv$shrcov+dixonenv$lrocks,family="negative_binomial")
plot(dfmv1.mv)
anova(dfmv1.mv)
```

## B Simple MDS & Permanova

Let's return to the @huttoUrbanOpenSpaces2021 example from the Chapter 15 exercises. There, we used similarity-based analyses to explore the relationship between frog assemblages in ponds and the degree of urbanization surrounding. This seems a question that could just as easily be examined using distances or dissimilarities.

Return to the data and assess whether frog assemblages (using the standardized abundance scale or presence-absence) differ with urbanization.

#### Did your conclusions differ from those obtained using RDA?

```{r}
df <- read_csv("../data/huttoamph.csv")
head(df,10)
#ponds 9 and 40 had no frogs. Remove for distance analysis
df <- df %>% 
  filter(Site!= 9 & Site !=40)
df
```

The explanation of the variables is in the previous chapter's exercises.

```{r}
df1 <- df[,-(1:2)]   #Stripped back file without labels, leaving only 
df1.bc <- vegdist(df1,'bray')
```

```{r}
#Run 2d first
df1.mds2 <- metaMDS(df1.bc,k=2,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1.mds2, main="Shepard plot")
df1.mds2
# Now look at 3d
df.mds3 <- metaMDS(df1.bc,k=3,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df.mds3, main="Shepard plot")
df.mds3
```

> 2-d is acceptable

```{r}
a<-as.data.frame(scores(df1.mds2))
a<-cbind(df[c(1:2)],a)   #Add site names & symbols from original data file
ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=type, ) )+
  geom_point()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=sym3,
                     name="Urbanization",
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )+
  theme_qk() + scale_color_uchicago()
```

```{r}
df1.ado <- adonis2(df1.bc~type,data=df,permutations=999)
print(df1.ado)
```

> Permanova detects a difference; MDS plot suggests low urbanization may be different from the other two, though worth looking at dispersion as well, as spread of this type is less than the other two on plot

> Repeat analysis with presence-absence

df1.jac \<- vegdist(df1,binary=TRUE,method='jaccard')

```{r}
#Run 2d first
df1.jac <- vegdist(df1,binary=TRUE,method='jaccard')
df1.mds2 <- metaMDS(df1.jac,k=2,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1.mds2, main="Shepard plot")
df1.mds2
# Now look at 3d
df.mds3 <- metaMDS(df1.jac,k=3,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df.mds3, main="Shepard plot")
df.mds3
```

> Again, stress OK with 2D, good with 3D. Look at 2D first

```{r}
a<-as.data.frame(scores(df1.mds2))
a<-cbind(df[c(1:2)],a)   #Add site names & symbols from original data file
ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=type, ) )+
  geom_point()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=sym3,
                     name="Urbanization",
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )+
  theme_qk() + scale_color_uchicago()
```

```{r}
df1.ado <- adonis2(df1.jac~type,data=df,permutations=999)
print(df1.ado)
```

> No separation seen on Presence-Absence

## C

@griffenSignificantEffectHIV2019 examined the oral microbiome of humans, with a focus on the effects of HIV and AntiRetroviral therapy (ART) on this microbiome. They described the microbiome of 341 patients, who fell into one of two categories: HIV^-^, and HIV+ with ART. They also matched their samples as far as possible for sex, along with other conditions that can influence oral microbiomes (*Candida* infection, current smoking). We'll use their records for these other categories as well. There were more HIV+ than - subjects, but within these groups, approximately equal numbers of two sexes, two *Candida* infection status, and two smoking categories.

The bacteriome was recorded separately using 16S RNA sequencing, which overed just over 600 taxa.

The data are available from their paper, as two Excel files in the supplementary information. The metadata gives HIV status, and a raft of demographic information. We'll just work with HIV, sex, *Candida*, and current smoking. A second sheet has the bacteriome. The code chunk below reads this file (from a Downloads folder - you'll need to modify the file location). It also screens the file for any bacterial taxa that were not present in this particular study, which reduces the bacterial taxa to 599.

```{r df}
library(readxl)
#Read in metadata. Lots of information we don't need, so a couple of iterations to get down to a few columns we want - HIV status, candida, current smoking, gender
df <- read_excel("../data/41598_2019_55703_MOESM3_ESM.xlsx", 
     range = "A1:S342", na = "NA")
df<-select(df, HIV, candida, gender, smoking_current)
head(df)
#df1 is the bacterial data
df1 <- read_excel("../data/41598_2019_55703_MOESM2_ESM.xlsx")
head(df1,10)
df1 <- df1 %>%
  select(where( ~ is.numeric(.x) && sum(.x) != 0))  #Drops any bacterial taxon not recorded in this study (i.e. where it's all zeroes)
df1 <- df1[,-1] #remove col1, which is sample ID
```

### Use a dissimilarity based approach to assess the combined effects of HIV-ART, sex, *Candida* infection, and current smoking on the bacteriome

**Do these factors act independently on the bacteriome?**

**Which effects are largest (use some graphical methods)?**

**First steps:** Think about standardization and which distance measure you'll use. Bray-Curtis seems common for these kind of data, and and counts of different taxa vary widely.

```{r BC}
df1s <- wisconsin(df1)   #Common to do some standardisation, and counts of different taxa vary widely
df1s.bc <- vegdist(df1s,'bray')   #With standardisation (wisconsin)
```

>Run factorial model using permanova, based on B-C

```{r}
df1.ado <- adonis2(df1s.bc~HIV*candida*gender*smoking_current,data=df,permutations=999)
print(df1.ado)
```

>Model shows main effects, but no interactions important (or at least, detected)

**Could you fit a simpler model to the data?**

>Run simpler model

```{r}
df2.ado <- adonis2(df1s.bc~HIV+candida+gender+smoking_current,data=df,permutations=999)
print(df2.ado)
```

>No change; not too surprising, as all four main effects were detected easily.

>Now go to data visualization

```{r}
#Run 3d first
df1s.mds3 <- metaMDS(df1s.bc,k=3,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1s.mds3, main="Shepard plot")
df1s.mds3
# Now look at 2d
df1s.mds2 <- metaMDS(df1s.bc,k=2,autotransform=FALSE,try=40,trymax=80,maxit=200)
stressplot(df1s.mds2, main="Shepard plot")
df1s.mds2
```


>3D model fits better than 2D. Stress for 2D above 0.2

> Start with plots where symbol colour indicates levels of one of the factors

```{r}
a<-as.data.frame(scores(df1s.mds3))
a<-cbind(df[c(1:4)],a)   #Add site names & symbols from original data file
p1<-ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=HIV) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=a, aes(x=NMDS1, y=NMDS3, color = HIV) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS3", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )

p1 + p2 + plot_layout(guides='collect') + plot_annotation(title="HIV status") & theme_qk() & scale_color_uchicago()

p1<-ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=candida) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=a, aes(x=NMDS1, y=NMDS3, color = candida) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS3", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )

p1 + p2 + plot_layout(guides='collect') + plot_annotation(title="Candida") & theme_qk() & scale_color_uchicago()

p1<-ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=gender) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=a, aes(x=NMDS1, y=NMDS3, color = gender) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS3", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )

p1 + p2 + plot_layout(guides='collect') + plot_annotation(title="Sex") & theme_qk() & scale_color_uchicago()

p1<-ggplot(data=a, aes(x=NMDS1, y=NMDS2, color=smoking_current) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=a, aes(x=NMDS1, y=NMDS3, color = smoking_current) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS3", x="MDS1")+
  scale_shape_manual(values=c(16,17),
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )

p1 + p2 + plot_layout(guides='collect') + plot_annotation(title="Current smoking") & theme_qk() & scale_color_uchicago()

```

>Try some visualizations of pairs of factors using MDS1 & MDS2 (while 3D is preferred, stress of 3D is around .15, vs 0.22, so not huge difference)
>Separate HIV+/-, then use symbol colour to separate second factor. 

```{r}
p1<-ggplot(data=subset(a, candida=="Yes"), aes(x=NMDS1, y=NMDS2, color=HIV) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1",
       title="Candida")+
  scale_shape_manual(
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=subset(a, candida =="No"), aes(x=NMDS1, y=NMDS2, color = HIV) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1",
       title = "No Candida")+
  scale_shape_manual(
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )
p_combined <- p1 + p2 + plot_layout(guides='collect') & theme_qk() & scale_color_uchicago()
p_ranges_x <- c(ggplot_build(p_combined[[1]])$layout$panel_scales_x[[1]]$range$range,
  ggplot_build(p_combined[[2]])$layout$panel_scales_x[[1]]$range$range)

p_ranges_y <- c(ggplot_build(p_combined[[1]])$layout$panel_scales_y[[1]]$range$range,
                ggplot_build(p_combined[[2]])$layout$panel_scales_y[[1]]$range$range)
p_combined & 
  xlim(min(p_ranges_x), max(p_ranges_x)) & 
  ylim(min(p_ranges_y), max(p_ranges_y))
```

```{r}
p1<-ggplot(data=subset(a, HIV=="Yes"), aes(x=NMDS1, y=NMDS2, color=candida) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1",
       title="HIV+")+
  scale_shape_manual(
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=subset(a, HIV =="No"), aes(x=NMDS1, y=NMDS2, color = candida) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1",
       title = "HIV-")+
  scale_shape_manual(
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )
p_combined <- p1 + p2 + plot_layout(guides='collect') & theme_qk() & scale_color_uchicago()
p_ranges_x <- c(ggplot_build(p_combined[[1]])$layout$panel_scales_x[[1]]$range$range,
  ggplot_build(p_combined[[2]])$layout$panel_scales_x[[1]]$range$range)

p_ranges_y <- c(ggplot_build(p_combined[[1]])$layout$panel_scales_y[[1]]$range$range,
                ggplot_build(p_combined[[2]])$layout$panel_scales_y[[1]]$range$range)
p_combined & 
  xlim(min(p_ranges_x), max(p_ranges_x)) & 
  ylim(min(p_ranges_y), max(p_ranges_y))
```

```{r}
p1<-ggplot(data=subset(a, HIV=="Yes"), aes(x=NMDS1, y=NMDS2, color = smoking_current) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1",
       title="HIV+")+
  scale_shape_manual(
                     guide =
                         guide_legend(label.theme = element_text(size=6), 
                                      title=NULL)
                     )
p2<-ggplot(data=subset(a, HIV =="No"), aes(x=NMDS1, y=NMDS2, color = smoking_current) )+
  geom_point()+
  stat_ellipse()+
  labs(y="MDS2", x="MDS1",
       title = "HIV-")+
  scale_shape_manual(
                     guide =
                         guide_legend(label.theme = element_text(size=6),
                                    title=NULL)
                     )
p_combined <- p1 + p2 + plot_layout(guides='collect') & theme_qk() & scale_color_uchicago()
p_ranges_x <- c(ggplot_build(p_combined[[1]])$layout$panel_scales_x[[1]]$range$range,
  ggplot_build(p_combined[[2]])$layout$panel_scales_x[[1]]$range$range)

p_ranges_y <- c(ggplot_build(p_combined[[1]])$layout$panel_scales_y[[1]]$range$range,
                ggplot_build(p_combined[[2]])$layout$panel_scales_y[[1]]$range$range)
p_combined & 
  xlim(min(p_ranges_x), max(p_ranges_x)) & 
  ylim(min(p_ranges_y), max(p_ranges_y))
```


## References
